Bounceback offers are offers to resort guests to entice you to book a return trip to WDW before you even leave from your current stay. They vary during the year, and are not always available.
You must book and deposit BEFORE check out. You usually see a flyer in your room or on the room TV, though sometimes no one (front desk, housekeeping, etc.) seems to know anything about them.

So the best way to make sure what BB is being offered during your stay is to call extension 8844 from your resort room.
You do not have to return to the same resort or category that you are currently staying at, and will have to put down a deposit before you leave.
You can only book BB rooms based on the current guests, i.e. no booking for other people who are not with you - though DISers have reported having the DH book one room and the DW another in order to have 2 BB rooms.
To give you an example of a BB, the current BB offer is:
Get 20% off a Select Disney VALUE Resort: 1/3-1/14/2010, 1/18-2/11, 2/15-3/27, 4/11-7/1, 7/5-11/23, 11/28-12/24/2010
Get 35% off a Select Disney MODERATE Resort: 1/3-1/14, 1/18-2/11, 2/15-3/27, 4/11-7/1, 7/5-11/23, 11/28-12/24/2010
Get 40% off WILDERNESS CABINS: 1/3-1/14, 1/18-2/11, 2/15-3/27, 4/11-7/1, 7/5-11/23, 11/28-12/24/2010
Get 40% off a Select Disney DELUXE Resort: 1/3-1/14, 1/18-2/11, 2/15-3/27, 4/11-7/1, 7/5-11/23, 11/28-12/24/2010
Get 45% off a Select Disney DELUXE VILLA Resort: 1/3-1/14, 1/18-2/11, 2/15-3/27, 4/11-7/1, 7/5-9/30/2010 (Offer excludes 3 bedroom grand villas) * Note: another nice DISer added these dates for the Villas 8/15-11/23 and 11/28-12/16/2010)
This BB offer will probably expire when people start arriving for
Free Dining in August, and a new one will probably start.
The last few years the BB during the FD period (Aug-Oct) is to be able to book a FD package a year ahead for the next years (2011) FD dates (usually Aug-Sept/Oct). You would put down a $200 deposit and have until 45 days prior to pay - no room discount, but you will have best resort availability and the guarantee of knowing you are getting FD saves a lot of anxiety wondering if they are going to offer it or not.
Based on this, the sad part for you is that:
1) you probably won't get any May BB dates when you go in September, but will probably get the FD BB. You probably can book a return FD package for next Aug-Sept/Oct 2011 (not May though)
2) even if you decide to do those dates instead of May, you probably can't book enough rooms to take everyone back with you unless you can all fit in 2 rooms (by using both names on the BB res)
BTW, May 2011 dates will probably be on the BB room discount offer that will open after the FD BB offer expires, probably in October. Maybe you'll have to talk DH into making a 2nd trip down to be able to book then
